[论文解读] Bacterial gene regulation in diauxic and nondiauxic growth

Atul Narang, Sergei S. Pilyugin|ArXiv.org|Aug 10, 2006

Protist diversity and phylogeny参考文献 2被引用 9

一句话总结

本文提出了一种细菌混合底物生长中基因调控的最小数学模型，表明仅通过酶诱导与稀释动力学——无需显式调控机制——即可解释分批生长、底物偏好性，甚至突变体中的“反向分批生长”现象。其关键贡献在于构建了一个分岔图，映射了参数空间中所有可能的底物消耗模式，揭示了底物偏好性本质上源于动力学竞争，而非调控优化。

ABSTRACT

When bacteria are grown on a mixture of two growth-limiting substrates, they exhibit a rich spectrum of substrate consumption patterns including diauxic growth, simultaneous consumption, and bistable growth. In previous work, we showed that a minimal model accounting only for enzyme induction and dilution captures all the substrate consumption patterns. Here, we construct the bifurcation diagram of the minimal model. The bifurcation diagram explains several general properties of mixed-substrate growth. (1) In almost all cases of diauxic growth, the "preferred" substrate is the one that, by itself, supports a higher specific growth rate. In the literature, this property is often attributed to optimality of regulatory mechanisms. Here, we show that the minimal model, which contains only induction, displays the property under fairly general conditions. This suggests that the higher growth rate of the preferred substrate is an intrinsic property of the induction and dilution kinetics.(2) The model explains the phenotypes of various mutants containing lesions in the regions encoding for the operator, repressor, and peripheral enzymes. A particularly striking phenotype is the "reversal of the diauxie" in which the wild-type and mutant strains consume the very same two substrates in opposite order. This phenotype is difficult to explain in terms of molecular mechanisms, but it turns out to be a natural consequence of the model. We show furthermore that the model is robust. The key property of the model, namely, the competitive dynamics of the enzymes, is preserved even if the model is modified to account for various regulatory mechanisms. Finally, the model has important implications for size regulation in development, since it suggests that protein dilution is one mechanism for coupling patterning and growth.

研究动机与目标

• 理解细菌在两种底物上生长时分批生长模式的起源。
• 确定诸如诱导剂排斥或cAMP激活等调控机制是否为解释底物消耗顺序所必需。
• 解释lac操纵子突变体中“反向分批生长”表型的成因，即突变株与野生型菌株以相反顺序消耗底物。
• 构建一个分岔图，基于模型参数映射所有可能的底物消耗模式。
• 证明仅基于酶诱导与稀释的最小模型具有鲁棒性，且无需显式调控即可解释多种实验表型。

提出的方法

• 基于酶诱导与稀释动力学构建最小数学模型，忽略显式调控反馈。
• 推导在混合底物条件下酶浓度的常微分方程组。
• 通过分析关键参数（如生长速率、诱导阈值）下稳态的数量与稳定性，构建分岔图。
• 利用零曲面的几何分析确定稳态的稳定性，应用广义Lotka-Volterra理论分析竞争物种。
• 对模型的根与判别式进行解析与数值分析，识别不同消耗模式之间的转变。
• 通过将预测表型（如反向分批生长）与lac操纵子突变体的实验观察进行比较，验证模型。

实验结果

研究问题

• RQ1 为何在无显式调控的情况下，支持更高比生长速率的底物在分批生长中总是首先被消耗？
• RQ2 如何通过最小模型解释“反向分批生长”表型——即突变株首先消耗非优选底物？
• RQ3 酶诱导与稀释动力学在决定底物消耗顺序方面起什么作用，且独立于分子调控机制？
• RQ4 在何种参数条件下，模型预测会同时消耗、分批生长或出现双稳态行为？
• RQ5 当引入已知的调控机制（如cAMP激活或诱导剂排斥）时，该最小模型是否仍具有鲁棒性？

主要发现

• 该模型表明，分批生长中的底物偏好性本质上源于酶诱导与稀释动力学，而非调控优化，解释了为何即使无显式调控，高生长速率底物仍被优先消耗。
• “反向分批生长”表型——即突变株首先消耗非优选底物——可自然地从模型的动力学中产生，尤其当酶诱导阈值不同时更为显著。
• 构建了一个分岔图，映射了参数空间中所有可能的底物消耗模式（同时消耗、分批生长、双稳态），揭示了行为之间的转变。
• 模型预测在临界参数值α*处，稳态方程出现重根，标志着从一个到两个非平凡稳态的转变，对应双稳态行为。
• 稳态的稳定性由非平凡零曲面的相对斜率决定：仅当第二个酶的零曲面比第一个更陡峭（负斜率更大）时，才存在稳定稳态。
• 当模型被修改以包含cAMP激活或诱导剂排斥等调控机制时，其仍保持鲁棒性，表明核心动力学由酶的竞争决定，而非调控细节。